Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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How is the slope between two points calculated?

(y₂-y₁)/(x₂-x₁)
y=mx+b
(a-b)(a²+ab+b²)
(a+b)(c+d)

The correct answer is: (y₂-y₁)/(x₂-x₁)

The slope between two points is calculated using the formula (y₂ - y₁) / (x₂ - x₁). This formula determines how steep a line is by measuring the vertical change (the difference in the y-coordinates) over the horizontal change (the difference in the x-coordinates) between the two points, often referred to as rise over run. This method provides a clear numerical representation of the incline of the line connecting the two points in a Cartesian plane. The result will indicate whether the line climbs or descends and at what rate, which is fundamental in algebra and geometry for understanding linear relationships. The other responses do not represent how to calculate the slope. For instance, while y = mx + b describes the slope-intercept form of a linear equation, it doesn’t calculate the slope between two specific points. Similarly, the other two formulas relate to algebraic expressions that do not pertain to the calculation of slope.